You can find basic instructions here and more details on the node page of the coin you're interested in. Since there is such a variation of available mining software, please consult their documentation on how to set it up using the values described on this site.

Payout occurs when the pool finds a block. The longer it takes to find a block, the longer it takes for payout to occur. The reward on the node's "Payout" tab is what you would receive if a block was found right now, based on the amount of work you've done in the past 24 hours in relation to the other miners at the pool. This means that your actual reward at the time of payout can vary a lot, depending on the pattern of the pool's hashrate. This is also why it's best to mine for at least the time it will take for the pool to find a couple of blocks.

Every node of the 0x0a pools uses P2PoolExtendedFrontEnd (github) as a frontend for the pool stats. You can find the node page by simply going to the pool's address, or click the link for "0x0a node" on the page for the coin of interest.

There's a finite amount of shares in the "sharechain" keeping track of everyone's 24-hour proportional reward. You need at least 1 to register as a worker at p2pool. This usually won't take long if your hashrate is reasonable, but might take a bit longer with a low hashrate. You can use the share estimate calculater on the node's page to get an estimate for when you'll show up.

0x0a is a big fan of open source and particularly FOSS / libre software. Cryptocurrency is extremely interesting to boot. Add P2Pool on top and there's a cake worth eating.